Ge'rard Cornue'jols

Combinatorial Optimization: Packing and Covering

CBMS-NSF Regional Conference Series in Applied Mathematics 74

This monograph presents new and elegant proofs of classical results and makes difficult results accessible. The integer programming models known as set packing and set covering have a wide range of applications. Sometimes, owing to the special structure of the constraint matrix, the natural linear programming relaxation yields an optimal solution that is integral, thus solving the problem. Sometimes, both the linear programming relaxation and its dual have integral optimal solutions. Under which conditions do such integrality conditions hold? This question is of both theoretical and practical interest. Min-max theorems, polyhedral combinatorics, and graph theory all come together in this rich area of discrete mathematics. This monograph presents several of these beautiful results as it introduces mathematicians to this active area of research.

To encourage research on the many intriguing open problems that remain, Dr. Cornue'jols is offering a $5000 prize to the first paper solving or refuting each of the 18 conjectures described in the book. To claim one of the prizes mentioned in the preface, papers must be accepted by a quality refereed journal (such as Journal of Combinatorial Theory B, Combinatorica, SIAM Journal on Discrete Mathematics, or others to be determined by Dr. Cornue'jols) before 2020. Claims must be sent to Dr. Cornue'jols at Carnegie Mellon University during his lifetime.

Audience

This book is appropriate for graduate students and faculty members in applied mathematics, operations research, and computer science with

About the Author

Dr. Ge'rard Cornue'jols, a professor at Carnegie Mellon University in Pittsburgh, Pennsylvania, is a past co-winner of the Lanchester Prize (1977) and the Fulkerson Prize (2000) and is a co-developer of MIPO, a mixed integer optimizer. He is editor-in-chief of Mathematics of Operations Research and is currently involved in research in combinatorial optimization, graph theory, and integer programming.

Contents

Preface; Chapter 1: Clutters; Chapter 2: T-Cuts and T-Joins; Chapter 3: Perfect Graphs and Matrices; Chapter 4: Ideal Matrices; Chapter 5: Odd Cycles in Graphs; Chapter 6: 0,+1 Matrices and Integral Polyhedra; Chapter 7: Signing 0,1 Matrices to Be Totally Unimodular or Balanced; Chapter 8: Decomposition by k-Sum; Chapter 9: Decomposition of Balanced Matrices; Chapter 10: Decomposition of Perfect Graphs; Bibliography; Index

2001 / xii + 132 pages / Softcover / ISBN 0-89871-481-8

Andreas D. Baxevanis, Genome Technology Branch, National Human Genome Research Institute, Bethesda, Maryland
B. F. Francis Ouellette, Centre for Molecular Medicine and Therapeutics, University of British Columbia, Vancouver, British Columbia

Bioinformatics:
A Practical Guide to the Analysis of Genes and Proteins, 2nd Edition

ISBN: 0-471-38390-2
Hardcover
ISBN: 0-471-38391-0
Softcover
Pages: 488

Copyright: 2001
"In this book, Andy Baxevanis and Francis Ouellette . . . have undertaken the difficult task of organizing the knowledge in this field in a logical progression and presenting it in a digestible form. And they have done an excellent job. This fine text will make a major impact on biological research and, in turn, on progress in biomedicine. We are all in their debt."--Eric Lander from the Foreword

Reviews from the First Edition

"...provides a broad overview of the basic tools for sequence analysis ... For biologists approaching this subject for the first time, it will be a very useful handbook to keep on the shelf after the first reading, close to the computer."--Nature Structural Biology

"...should be in the personal library of any biologist who uses the Internet for the analysis of DNA and protein sequence data." --Science

"...a wonderful primer designed to navigate the novice through the intricacies of in scripto analysis ... The accomplished gene searcher will also find this book a useful addition to their library ... an excellent reference to the principles of bioinformatics."--Trends in Biochemical Sciences

This new edition of the highly successful Bioinformatics: A Practical Guide to the Analysis of Genes and Proteins provides a sound foundation of basic concepts, with practical discussions and comparisons of both computational tools and databases relevant to biological research.

Equipping biologists with the modern tools necessary to solve practical problems in sequence data analysis, the Second Edition covers the broad spectrum of topics in bioinformatics, ranging from Internet concepts to predictive algorithms used on sequence, structure, and expression data. With chapters written by experts in the field, this up-to-date reference thoroughly covers vital concepts and is appropriate for both the novice and the experienced practitioner. Written in clear, simple language, the book is accessible to users without an advanced mathematical or computer science background. This new edition includes:
All new end-of-chapter Web resources, bibliographies, and problem sets
Accompanying Web site containing the answers to the problems, as well as links to relevant Web resources
New coverage of comparative genomics, large-scale genome analysis, sequence assembly, and expressed sequence tags
A glossary of commonly used terms in bioinformatics and genomics

Bioinformatics: A Practical Guide to the Analysis of Genes and Proteins, Second Edition is essential reading for researchers, instructors, and students of all levels in molecular biology and bioinformatics, as well as for investigators involved in genomics, positional cloning, clinical research, and computational biology.

Mark M. Meerschaert, Univ. of Nevada, Reno, Nevada
Hans-Peter Scheffler, Univ. of Dortmund, Germany

Limit Distributions for Sums of Independent Random Vectors:
Heavy Tails in Theory and Practice

ISBN: 0-471-35629-8
Hardcover
Pages: 512

Copyright: 2001
A comprehensive introduction to the central limit theory-from foundations to current research

This volume provides an introduction to the central limit theory of random vectors, which lies at the heart of probability and statistics. The authors develop the central limit theory in detail, starting with the basic constructions of modern probability theory, then developing the fundamental tools of infinitely divisible distributions and regular variation. They provide a number of extensions and applications to probability and statistics, and take the reader through the fundamentals to the current level of research.

In synthesizing results from nearly 200 research papers and presenting them in a self-contained form, authors Meerschaert and Scheffler have produced an accessible reference that treats the central limit theory honestly and focuses on multivariate models. For researchers, it provides an efficient and logical path through a large collection of results with many possible applications to real-world phenomena. Limit Distributions for Sums of Independent Random Vectors includes a coherent introduction to limit distributions and these other features:
A self-contained introduction to the multivariate problem
Multivariate regular variation for linear operators, real-valued functions, and Borel Measures
Multivariate limit theorems: limit distributions, central limit theorems, and related limit theorems
Real-world applications

Limit Distributions for Sums of Independent Random Vectors is a comprehensive reference that provides an up-to-date survey of the state of the art in this important research area.
Subject: College Probability and Statistics / PROBABILITY AND MATH STATISTICS / PROBABILITY & STAT FOR ENGINEERS

Series Title:Wiley series in Probability and Statistics

Attila Nagy
Budapest University of Technology and Economics, Hungary

Special Classes of Semigroups

ADVANCES IN MATHEMATICS Volume 1

In semigroup theory there are certain kinds of band decompositions, which are very useful in the study of the structure semigroups. There are a number of special semigroup classes in which these decompositions can be used very successfully. The book focuses attention on such classes of semigroups. Some of them are partially discussed in earlier books, but in the last thirty years new semigroup classes have appeared and a fairly large body of material has been published on them. The book provides a systematic review on this subject. The first chapter is an introduction. The remaining chapters are devoted to special semigroup classes. These are Putcha semigroups, commutative semigroups, weakly commutative semigroups, R-Commutative semigroups, conditionally commutative semigroups, RC-commutative semigroups, quasi commutative semigroups, medial semigroups, right commutative semigroups, externally commutative semigroups, E-m semigroups, WE-m semigroups, weakly exponential semigroups, (m,n)-commutative semigroups and n(2)-permutable semigroups.

Audience: Students and researchers working in algebra and computer science.
Contents
Preface. 1. Preliminaries. 2. Putcha semigroups. 3. Commutative semigroups. 4. Weakly commutative semigroups. 5. R-, L-, H-commutative semigroups. 6. Conditionally commutative semigroups. 7. RC-commutative semigroups. 8. Quasi commutative semigroups. 9. Medial semigroups. 10. Right commutative semigroups. 11. Externally commutative semigroups. 12. E-m semigroups, exponential semigroups. 13. WE-m semigroups. 14. Weakly exponential semigroups. 15. (m,n)-commutative semigroups. 16. n(2)-permutable semigroups. Bibliography. Index.

Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-6890-8
May 2001, 280 pp.

Christodoulos A. Floudas Princeton University, NJ
Panos M. Pardalos Dept. of Industrial & Systems Engineering, University of Florida, Gainesville,

Encyclopedia of Optimization

Optimization problems are ubiquitous in the mathematical modeling of real world systems and cover a very broad range of applications. These applications arise in all branches of Engineering, Computer Science, Economics, Finance, Operations Research and Management Science, Chemistry, Materials Science, Astronomy, Physics, Structural and Molecular Biology, and Medicine.

The Encyclopedia of Optimization aims at serving as an important reference for all parts of optimization. It is directed to a diverse audience of students, scientists, engineers and in general to any decision maker and problem solver in academia, business, industry, and government who is concerned with aspects of optimization theory, algorithms, and applications.

There are two main types of articles in the Encyclopedia of Optimization. The first type consists of survey-expository type articles regarding various topics of optimization of general interest. The second type contains more detailed concrete problems, techniques, or applications. The Encyclopedia of Optimization also contains articles that provide historical perspectives and selected biographical entries.

All articles provide an introduction and motivation for the subjects, present the important contributions and illustrations, and contain a list of references that can be used as pointers for more detailed information on the subject. Besides the five volumes of articles, a separate volume of a cumulative index with thorough cross-referencing is provided that can serve as a useful tool of searching.

Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-6932-7
August 2001, 3200 pp.

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